JDOI variance reduction method and the pricing of American-style options
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JDOI variance reduction method and the pricing of American-style options. / Auster, Johan; Mathys, Ludovic; Maeder, Fabio.
In: Quantitative Finance, Vol. 22, No. 4, 2022, p. 639-656.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - JDOI variance reduction method and the pricing of American-style options
AU - Auster, Johan
AU - Mathys, Ludovic
AU - Maeder, Fabio
PY - 2022
Y1 - 2022
N2 - This article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under (time-homogeneous) Lévy stochastic differential equations. The resulting Jump Diffusion Operator Integral (JDOI) method can be combined with numerous Monte Carlo-based stopping-time algorithms, including the ubiquitous least-squares Monte Carlo (LSMC) algorithm of Longstaff and Schwartz (cf. Carriere (1996) and Longstaff and Schwartz (2001)). We exemplify the usefulness of our theoretical derivations under a concrete, though very general jump-diffusion stochastic volatility dynamics and test the resulting LSMC-based version of the JDOI method. The results provide evidence of a strong variance reduction when compared with a simple application of the LSMC algorithm and proves that applying our technique on top of Monte Carlo-based pricing schemes provides a powerful way to speed-up these methods.
AB - This article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under (time-homogeneous) Lévy stochastic differential equations. The resulting Jump Diffusion Operator Integral (JDOI) method can be combined with numerous Monte Carlo-based stopping-time algorithms, including the ubiquitous least-squares Monte Carlo (LSMC) algorithm of Longstaff and Schwartz (cf. Carriere (1996) and Longstaff and Schwartz (2001)). We exemplify the usefulness of our theoretical derivations under a concrete, though very general jump-diffusion stochastic volatility dynamics and test the resulting LSMC-based version of the JDOI method. The results provide evidence of a strong variance reduction when compared with a simple application of the LSMC algorithm and proves that applying our technique on top of Monte Carlo-based pricing schemes provides a powerful way to speed-up these methods.
KW - Faculty of Science
KW - American options
KW - Lévy models
KW - Stochastic volatility
KW - Variance reduction
KW - Monte Carlo methods
U2 - 10.1080/14697688.2021.1962959
DO - 10.1080/14697688.2021.1962959
M3 - Journal article
VL - 22
SP - 639
EP - 656
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 4
ER -
ID: 280282578